Revisiting Entanglement Entropy of Lattice Gauge Theories

Abstract

Casini et al raise the issue that the entanglement entropy in gauge theories is ambiguous because its definition depends on the choice of the boundary between two regions.; even a small change in the boundary could annihilate the otherwise finite topological entanglement entropy between two regions. In this article, we first show that the topological entanglement entropy in the Kitaev model which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiement, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.

15 pages, 3 figures

References in corpus (2)

• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• String-Net Models with $Z_N$ Fusion Algebra

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• Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization
• Dynamical Edge Modes in $p$-form Gauge Theories
• De Sitter Horizon Edge Partition Functions
• Gravitons on Nariai Edges